First, I'm making the assumption that you are looking at new. Older models changes the choices somewhat.
Most 350/3500s have technically more payload capacity than the F450 pickup bed model. If you go over a 3500 lb dry camper, you will likely push the F450 pickup bed payload. The truck is heavier than the 350, but with higher axle capacity, better brakes, and better turn radius. A good fit for my 9 1/2 heavy camper and just under GVWR for me with full fluids and loaded how we camp.
If you go heavier and want the best brakes, I think you have to go 550/5500 or possibly 450 with flatbed. The suspension is different on the flatbed models compared to the pickup bed, and they have more payload capacity. The 350/3500s have great payload in the newer models.
The downsides are the most common gearing/mpg is probably different from 350-550 although you'll have to compare to models to find out. Custom beds are very expensive as in around $8000. They are very nice but for my use, they didn't make sense.
If you want the most storage capacity, you also need to go flatbed which would be a big plus for full timing.